Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets

TL;DR

This paper uses density matrix renormalization group calculations to confirm that the Haldane phase in certain one-dimensional antiferromagnetic chains remains stable despite randomness, supporting a longstanding conjecture.

Contribution

It provides numerical evidence confirming the stability of the Haldane phase against randomness in specific quantum spin chains.

Findings

Haldane phase remains stable under any randomness strength

String order parameter remains non-zero in the presence of disorder

Energy gap distribution indicates robustness of the phase

Abstract

It is conjectured that the Haldane phase of the S=1 antiferromagnetic Heisenberg chain and the $S=1/2$ ferromagnetic-antiferromagnetic alternating Heisenberg chain is stable against any strength of randomness, because of imposed breakdown of translational symmetry. This conjecture is confirmed by the density matrix renormalization group calculation of the string order parameter and the energy gap distribution.